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A stationary Poisson departure process from a minimally delayed infinite server queue with non-stationary Poisson arrivals

Part of: Special processes Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

John A. Barnes  and
Richard Meili
John A. Barnes*
Affiliation:
Virginia Commonwealth University
Richard Meili*
Affiliation:
Virginia Commonwealth University
*
∗Postal address: Department of Mathematical Sciences, Virginia Commonwealth University, 1015 West Main Street, Box 2014, Richmond, VA 23284-2014, USA.
∗Postal address: Department of Mathematical Sciences, Virginia Commonwealth University, 1015 West Main Street, Box 2014, Richmond, VA 23284-2014, USA.
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Abstract

The points of a non-stationary Poisson process with periodic intensity are independently shifted forward in time in such a way that the transformed process is stationary Poisson. The mean shift is shown to be minimal. The approach used is to consider an Mt/Gt/∞ queueing system where the arrival process is a non-stationary Poisson with periodic intensity function. A minimal service time distribution is constructed that yields a stationary Poisson departure process.

Keywords

POISSON PROCESSNON-STATIONARY POISSON PROCESSINFINITE SERVER QUEUE

MSC classification

Primary: 60G55: Point processes 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 767 - 772
Copyright
Copyright © Applied Probability Trust 1997 

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References

Eick, S. G., Massey, W. A. and Whitt, W. (1993) The physics of the Mt/G/8 queue. Operat. Res. 41, 731–742.CrossRefGoogle Scholar
Foley, R. D. (1982) The non-homogeneous M/G/8 queue. Opsearch 19, 40–48.Google Scholar
Foley, R. D. (1986) Stationary. Poisson departure processes from non-stationary queues. J. Appl. Prob. 23, 256–260.CrossRefGoogle Scholar
Green, L., Kolesar, P. and Svoronos, A. (1991) Some effects of nonstationarity on multiserver Markovian queueing systems. Operat. Res. 39, 502–511.CrossRefGoogle Scholar
Ross, S. (1978) Average delay in queues with non-stationary Poisson arrivals. J. Appl. Prob. 15, 602–609.CrossRefGoogle Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar